Question

If the slope of one of the lines given by $k{x}^2+4xy-y^2=0$ is three times the other than k is equal to:

• A. 3
• B. 2
• C. -2
• D. -3

Answer 1

The correct option is D -3

Given $k{x}^2+4xy-y^2=0$

Comparing with $a{x}^2+2hxy+b{y}^2=0$

Here $a=k,2h=4,andb=-1$

Let $m_1$ and $m_2$ be the slopes of the two lines represented by given equation

$m_1+m_2=\frac{-2h}{b}=\frac{-4}{-1}=4$

and $m_1.m_2=\frac{a}{b}=\frac{k}{-1}=-k$

Given that $m_1=3m_2$

Now,

$m_1+m_2=4$

$3m_2+m_2=4$

$4m_2=4$

$m_2=1$

$m_1=3m_2=3\times 1=3$

Now,

$m_1.m_2=-k$

$\left(3\right)\left(1\right)=-k$

$\therefore k=-3$